How to have free upgrade from IMac OS X version 10.7.5?

The year model of your iMac absolutely determines how far you can upgrade. Doing "About this Mac" from your Apple menu will show that. Example from OS 10.8:

Please tell us what your computer shows for the line I indicated with the red arrow. Note that any modifiers like Early, Mid, or Late are important to include.

I doubt that any Mac still running 10.7 can be fully upgraded to current OS levels. The newest iMacs that shipped with 10.7 are the Late 2011 models and they max out at OS 10.13, far below current levels. Above 10.13 are 10.14; 10.15, 11.x, and 12.x.

Older macOS version but still newer than 10.7 are available free through links in this Apple article. You must use Safari for any downloads:

How to get old versions of macOS - Apple Support